论文标题
Q二项式定理的概括
A Generalization of q-Binomial Theorem
论文作者
论文摘要
通过使用刘的$ q $ - 派对差分方程理论，我们证明，如果几个变量中的分析功能满足$ q $ - 优势差分方程的系统，那么并且仅当它才能根据均质$（q，q，c）$ -Al-Salam-salam-Carlitz Polynomials进行扩展。作为一个应用程序，我们证明了$ c \ neq0 $和$ \ max \ {| cq |，| x | \} <1 $，\ begin {align*} \ sum_ {n = 0}^{\ infty} {\ infty} \ frac {（a; q）_n; q） } {（cq; q）_n} x^n =（ax/c; q）_ {\ infty} \ sum_ {n = 0}^{\ infty} \ frac {x^n} {（x^n} {（cq; q）定理。
By using Liu's $q$-partial differential equations theory, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, if and only if it can be expanded in terms of homogeneous $(q,c)$-Al-Salam-Carlitz polynomials. As an application, we proved that for $c\neq0$ and $\max \{|cq|,|x|\}<1$, \begin{align*} \sum_{n=0}^{\infty} \frac{ (a;q)_n }{(cq;q)_n}x^n=(ax/c;q)_{\infty} \sum_{n=0}^{\infty} \frac{x^n}{(cq;q)_n}, \end{align*} which is a generalization of famous $q$-binomial theorem or so-called Cauchy theorem.
